{"paper":{"title":"Homogeneity of Inverse Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Thomas Quinn-Gregson","submitted_at":"2017-06-03T16:38:22Z","abstract_excerpt":"An inverse semigroup $S$ is a semigroup in which every element has a unique inverse in the sense of semigroup theory, that is, if $a \\in S$ then there exists a unique $b\\in S$ such that $a = aba$ and $b = bab$. We say that an inverse semigroup $S$ is a homogeneous (inverse) semigroup if any isomorphism between finitely generated (inverse) subsemigroups of $S$ extends to an automorphism of $S$. In this paper, we consider both these concepts of homogeneity for inverse semigroups, and show when they are equivalent. We also obtain certain classifications of homogeneous inverse semigroups, in parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00975","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}